homework3[1] - Homework 3 Spring 2010 AMCS 260/CS 260...

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Homework 3 Spring 2010: AMCS 260/CS 260: Design and Analysis of Algorithms Instructions: This homework is due on Tuesday, April 20, 2010 in class. You should work individually (not in groups) and submit it handwritten on A4-size papers. Write your name clearly on top of every page as well as the total number of pages. You may have queries related to this homework which should be directed to the TAs. Office Hours of TAs Shahid Hussain Mondays 2:30pm – 4:30pm [email protected] Tuesdays 2:00pm – 4:00pm Abdulaziz Alkhalid Satudays 10:00am – 12:00pm [email protected] Sundays 10:00am – 12:00pm 1. Given a sequence of matrices A, B, C and D with dimensions 10 × 100, 100 × 10, 10 × 100 and 100 × 10, respectively. (a) How may scalar multiplications and additions are needed to compute the product A ( BC ) using the conventional matrix multiplication algorithm? (b) A chain of matrices is fully parenthesized if it is either single matrix or a product of two fully parenthesized matrix products. How many different parenthesizations are there for ABCD ? (c) Find an optimal parenthesization for the given chain of matrices
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